Distorted plane as image
Alpha values range from 0-255.  Your image editing program is hiding pixels with very low values such as 1-3 into that background checkerboard pattern.  Blender is expecting 0 for complete transparency.  

Open image in GIMP, use the magic wand tool to select transparent area, then click Delete key.

File >> Export As... and give it a new name, or Overwrite PNG if you are satisfied with results.